Confidence Interval Calculator for Conversion Rates

A conversion rate measured on a sample is an estimate. Another sample of the same size would give a slightly different rate. The confidence interval shows how far the true rate could plausibly be from the one you measured.

The more participants, the narrower the interval. The higher the confidence level, the wider it gets: 99% casts a wider net than 90%.

The "Plan precision" tab answers the reverse question: how many participants you need so that the interval reaches no further than a chosen margin on each side.

A landing page had 1,000 visitors and 50 sign-ups, a rate of 5.0%.

The 95% confidence interval runs from 3.8% to 6.5%. The range reaches 1.2 points below the rate and 1.5 points above it: near 0% intervals are uneven, because the rate cannot fall below zero.

To pin a rate of about 5% down to ±1 percentage point at 95%, plan for about 1,825 visitors.

The calculator uses the Wilson score interval without continuity correction. With p = x / n and q the normal quantile for the chosen level (1.96 for 95%):

denom = 1 + q² / n
centre = (p + q² / (2n)) / denom
half = q × √(p(1 − p) / n + q² / (4n²)) / denom
lower = centre − half,  upper = centre + half

The common textbook formula, rate ± 1.96 × standard error, gives impossible ranges below 0% for small rates and a zero-width range at 0 conversions. The Wilson interval stays between 0% and 100%, gives a real upper bound at 0 conversions, and is also what the A/B test results calculator builds on, so the two tools agree.

Planning uses the normal approximation n = q² × p(1 − p) / m², rounded up, where m is the margin as a proportion.

What does a 95% confidence interval mean?

It describes the method, not this one range: if you repeated the measurement many times, about 95% of the intervals built this way would contain the true rate. It does not mean there is a 95% chance the true rate is in the range you see, and values near the middle are not guaranteed to be more likely.

Why is the range uneven around a small rate?

A rate cannot go below 0%. Near zero the interval has more room above the rate than below it, so it stretches upwards. The same happens near 100% in the other direction.

Why not just use rate ± 2 × standard error?

That formula works for rates far from 0% and 100% and large samples. For small rates it can give a negative lower bound, and at 0 conversions it gives a range of zero width, which suggests certainty you do not have. The Wilson interval avoids both problems.

Which level should I choose: 90, 95 or 99%?

95% is the common default. Choose 99% when being wrong is costly and you can accept a wider range, and 90% for a quick, rougher read. Pick the level before looking at the data.

The interval is too wide. What can I do?

Collect more data: the width shrinks roughly with the square root of the number of participants, so halving it takes about four times as many. The "Plan precision" tab tells you how many you need for a given margin.

Can I compare two variants with two intervals?

Not reliably. Two intervals can overlap even when the difference between the variants is significant. To compare two variants, use an interval for the difference itself, which the A/B test results calculator gives you.

For the difference between A and B, with its interval and a p-value: A/B test results calculator

• confidence interval (CI)
• standard error (SE)

• A/B test results calculator

  Reading the results of a finished test with two variants.

• A/B test sample size calculator

  Planning for two variants (A/B) before the test starts.

• Survey sample size calculator

  Planning how many survey answers you need, or how precise they are.